Multidimensional characterization of asymptotically Is2- equivalent sequences

Abstract

In 1951 Fast [12] introduced the concept statistical convergence of sequences which is a generalization of convergence. Afterward, Kostyrko et al. [14] extended the notion of statistical convergence to ideal convergence and established some basic theorems. Taking inspiration from this new approach, in this paper we introduce the matrix characterization of asymptotically I-2-equivalent and asymptotically I-2- statistical equivalent double sequences with an up-to-date perspective on multidimensional matrix transformation. Consequently, we will obtain conditions on (a(m,n,k,l)) which assure us that the transformation is asymptotically I-2-regular. This will be accomplished through a series of regularity-type theorems.